The chicks and hen will need to eat chick starter - layer feed has too much calcium in it for chicks. If the broody drinks from the nipple waterers then she will teach her chicks to - you'll just need to make sure they have something they can climb up on to reach the nipples. Alternatively you could give them a shallow dish of water that has stones or marbles in it to drink from. Chicks can drown easily so the marbles/stones prevent this.
And yes, lockdown is day 19 to hatch. Take out the turners before lockdown as moving the eggs around during those last few days can cause the chicks to malposition and get stuck or pip at the wrong end of the egg. Good luck!